Swimming in the hotel pool I saw these depth markers. As a math teacher, they made me a bit uneasy. What do you notice in the photos below? What do you wonder?

The Shallow End

The Deep End

Just look at those significant digits. They look so precise. I first thought... going from the shallow end to the deep end, it gets 1 foot / 0.2 metres deeper. That must mean that 1 ft = 0.2 m right? But then if 1 ft is 0.2 m then shouldn't 3 ft in the shallow end be 0.6 m instead of 1.0 m?

So I looked at it another way... 1 m is the same as 3 ft... So 1 ft must be about 0.33 m. Which would make 4 ft equal to about 1.33 m not the 1.2 m as shown. But I know that a meter stick is shorter than a yard stick so this is just an approximation. No problem, they just rounded off both values.

Then I had a moment of doubt... in the shallow end the values are in a ratio of 1/3 and in the deep end the values are in a ratio of 4/12 which is also 1/3 so shouldn't this work out? Then I realized the errors and misconceptions in this line of thinking.

​So looking at these signs I can find that 1 ft is either 0.2 m, 0.3 m or 0.33 repeating m. In case you're wondering, 1 metre is more accurately about 3.28084 feet. Given this, I really think the shallow end should say 0.9 metres instead of 1.0 metres (or perhaps the 3 ft should be 3 ft-3 inches instead).

Other Linear Conversions

Today, as I was driving around, I looked more closely at the clearance signs that I passed under. There doesn't seem to be much consistency in the units used or precision. Do people with tall cars know the height of their car? I just know that I'm about 6 ft tall and my car is shorter than I am. Of course you can always just wing it. If you clear the warning bar, you're good to go. Anyway, I know for sure that my car is less than 11 foot 8 if I ever end up in North Carolina.

The airport parking garage.

The IKEA parking lot.

I also saw this at the airport. Is it exactly 6 cm or exactly 2.4 inches? They are not the same length although they are fairly close. They are about 1 mm different which is probably about the width of that thick orange line. I'm guessing that's not a coincidence.

Carry on restrictions at the airport.

I saw this relatively accurate sign at a parking garage today so I took a photo. 6'0" is approximately 1.8288 metres so these values are the closest I've seen.

Nova Scotia Mathematics Curriculum OutcomesMathematics 10 M02 - Students will be expected to apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.Mathematics at Work 10 M01 - Students will be expected to demonstrate an understanding of the International System of Units (SI) by describing the relationships of the units for length, area, volume, capacity, mass, and temperature and applying strategies to convert SI units to imperial units. ​Mathematics Essentials 10 D1 - Demonstrate a working knowledge of the metric system and imperial system.